Variable selection in a flexible parametric mixture cure model with interval‐censored data

Abstract

In standard survival analysis, it is generally assumed that every individual will experience someday the event of interest. However, this is not always the case, as some individuals may not be susceptible to this event. Also, in medical studies, it is frequent that patients come to scheduled interviews and that the time to the event is only known to occur between two visits. That is, the data are interval‐censored with a cure fraction. Variable selection in such a setting is of outstanding interest. Covariates impacting the survival are not necessarily the same as those impacting the probability to experience the event. The objective of this paper is to develop a parametric but flexible statistical model to analyze data that are interval‐censored and include a fraction of cured individuals when the number of potential covariates may be large. We use the parametric mixture cure model with an accelerated failure time regression model for the survival, along with the extended generalized gamma for the error term. To overcome the issue of non‐stable and non‐continuous variable selection procedures, we extend the adaptive LASSO to our model. By means of simulation studies, we show good performance of our method and discuss the behavior of estimates with varying cure and censoring proportion. Lastly, our proposed method is illustrated with a real dataset studying the time until conversion to mild cognitive impairment, a possible precursor of Alzheimer's disease. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Recipient obesity does not affect survival after deceased donor liver transplantation for hepatocellular carcinoma. A national retrospective cohort study in the United States

“…Flexible parametric models using restricted cubic spline functions were used to model and plot patients' survival and the non-linear effect of BMI with the Hazard ratio (HR). [16][17][18][19] All hazard ratios (HR) and adjusted HR (AHR) referred to the baseline value of normal weight recipients (BMI 18.5-25). Pretransplant characteristics utilized in the models were selected a priori.…”

Cure Models in Survival Analysis

“…When a parametric form is however assumed for the latency, the Liu et al (2012) approach is not natural because the complete-data likelihood is not used. For mixture cure models with a parametric latency, Scolas et al (2016) proposed a method based on a penalized likelihood in the context of interval-censored cure data. Adaptive LASSO penalties are assumed, one for each part of the model, and the penalized likelihood is derived from (5).…”

Diagnostic checks in mixture cure models with interval-censoring

“…Clearly, such time-to-event data can be both right-censored since some patients have not yet experienced MCI conversion at the end of the follow-up period, and interval-censored since MCI conversion is typically known to have occurred between two successive follow-up visits. As pointed out in [Scolas et al, 2015], an additional feature of these data is that a fraction of the patients will never convert to MCI, whatever the length of follow-up. In the statistical literature, this kind of patients are referred to as "cured individuals", or "longterm survivors" or "non-susceptibles" ( [Maller and Zhou, 1996]).…”